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JEE MainPhysicsCapacitance

A capacitor is constructed with a flat bottom plate of area A and a stepped top plate. The stepped plate has three horizontal sections, each of area A 3 . The separations between the bottom plate and the three sections are d , 2d , and 3d respectively. The gap of the first section (with separation d ) is completely filled with a dielectric material of dielectric constant K = 2 . The other two gaps are filled with air

Options

  1. A11 ₀ A 18 d
  2. B11 ₀ A 9 d
  3. C2 ₀ A 33 d
  4. D17 ₀ A 18 d

Correct answer

D. 17 ₀ A 18 d

Step-by-step solution

The arrangement can be modeled as three capacitors connected in parallel, each having an area of A 3 . The first capacitor has a plate separation d and is filled with a dielectric of K = 2 . Its capacitance is: C₁ = K ₀ ( A 3 ) d = 2 ₀ A 3d The second capacitor has a plate separation 2d and is filled with air. Its capacitance is: C₂ = ₀ ( A 3 ) 2d = ₀ A 6d The third capacitor has a plate separation 3d and is filled with air. Its capacitance is: C₃ = ₀ ( A 3 ) 3d = ₀ A 9d Since they are in parallel, the equivalent c

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